A263887 Number of permutations of [n] containing exactly three occurrences of the consecutive pattern 132.

15, 576, 13572, 259968, 4532034, 75929856, 1259571660, 21052915200, 358291184565, 6248298977280, 112089186363960, 2073140406374400, 39582481045276260, 780630651563728896, 15904712294529556680, 334724021030855393280, 7274246960518735730715

Offset

7,1

Links

Alois P. Heinz, Table of n, a(n) for n = 7..200

Formula

a(n) = A197365(n,3).

Example

a(7) = 15: 1325476, 1326475, 1327465, 1425376, 1426375, 1427365, 1524376, 1526374, 1527364, 1624375, 1625374, 1627354, 1724365, 1725364, 1726354.
a(8) = 576: 12436587, 12437586, 12438576, ..., 81724365, 81725364, 81726354.
a(9) = 13572: 123547698, 123548697, 123549687, ..., 981724365, 981725364, 981726354.

Maple

b:= proc(u, o, t) option remember; series(`if`(u+o=0, 1,
      add(b(u-j, o+j-1, 0)*`if`(j<=t, x, 1), j=1..u)+
      add(b(u+j-1, o-j, j-1), j=1..o)), x, 4)
    end:
a:= n-> coeff(b(n, 0$2), x, 3):
seq(a(n), n=7..30);

Crossrefs

Column k=3 of A197365.

Sequence in context: A329122 A027534 A001236 * A183546 A179895 A343074

Adjacent sequences: A263884 A263885 A263886 * A263888 A263889 A263890

Keyword

nonn

Author

Alois P. Heinz, Oct 28 2015

Status

approved